As the simplest topological field theory, Chern-Simons theory[1]} with Abelian gauge group has a clear geometrical meaning: it counts the linking number of loops[2]}[3]}. However, there are ambiguities regarding the self-linking, and singularities also arise when loops intersect[2]}[5]}. The former is called 'framing anomaly', and it may have important contribution to thermal Hall conductivity, Hall viscosity, and linear responses of fractional quantum Hall systems[6]}[7]}. One way to regularize such ambiguities is to define the theory on a lattice. The lattice approach also makes it possible to study Chern-Simons theory with discrete gauge groups like \(\mathbb {Z}_n\) , which has no clear analog in continuous spacetime. Morever, the lattice construction of Chern-Simons theory can also be used to formulate a composite fermion description for fractional Chern insulators[8]}.
